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unscientific
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Homework Statement
For a spin 1/2 system, the eigenstates of z-component of the angular-momentum operator Sz are given by:
[tex]S_z |\pm> = \pm \frac{\hbar}{2}|\pm>[/tex]
Suppose at time t, the state of the system is given by:
[tex]|\psi> = a|+> + b|-> [/tex]
If Sz is measured, what are the possible results of measurement and their probabilities?
Homework Equations
The Attempt at a Solution
Possibilities: State |+> or |->.
[tex]<+|S_z|\psi> = \frac{\hbar}{2} <+|\psi> = \frac{\hbar}{2}a [/tex]
Probability of |+> state = ##\frac{\hbar ^2 a^2}{4}##
Similarly,
Probability for |-> state = ##\frac{\hbar ^2 b^2}{4}##
This is weird, as the probability should just be ##a^2## and ##b^2## correspondingly?